This invention is a method for designing a lens to provide an optimal corrective lens-eye system having minimal image aberrations and the resulting lens having an aspheric surface for use as an contact, intraocular or spectacle lens, particularly a lens in which the surface has a hyperbolic or parabolic curvature.
The curvature of a conventional lens surface may be described in terms of "conic sections." The family of conic sections includes the sphere, parabola, ellipse, and hyperbola. All rotationally symmetric conic sections may be expressed in terms of a single equation: ##EQU1## where X is the aspheric surface point at position Y, r is the central radius, and the kappa factor, .kappa., is the aspheric coefficient.
Other conic constants or aspheric coefficients include the eccentricity, e, which relates to .kappa. by the equation .kappa.=-e.sup.2, and the rho factor, .rho., defined as (1-e.sup.2).
The value of the aspheric coefficient determines the form of the conic section. For a sphere, e=0 and x=0. An ellipse has an eccentricity between 0 and 1 and a .kappa. between 0 and -1. A parabola is characterized by an e=1 (.kappa.=-1). For a hyperbola, e is greater than 1 and .kappa. is less than negative one.
Conventionally, most lens surfaces are spherical or near-spherical in curvature. Theoretically, for an infinitely thin lens, a spherical curvature is ideal to sharply focus the light passing through the lens. However, the curvatures and thicknesses of a real lens produce well-known optical aberrations, including spherical aberration, coma, distortion, and astigmatism; i.e., light from a point source passing through different areas of the lens that does not focus at a single point. This causes a certain amount of blurring. Furthermore, purely spherical lenses are not suitable for correcting astigmatic vision or for overcoming presbyopia.
For this reason, many different types of lenses have been designed for the purpose of minimizing spherical aberration, correcting ocular astigmatism, or providing a bifocal effect that allows the nonaccommodative eye to see objects both near and far. Unfortunately, current designs suffer from serious drawbacks, such as producing blurred or hazy images, or inability to provide sharp focusing at every visual distance.
Aspheric lenses having elliptical surfaces have been used to reduce optical aberrations. Some well known examples are the use of parabolic objective mirrors in astronomical telescopes and the use of ellipses of low eccentricity to correct for aberrations of a contact lens.
The design of an aspheric lens in isolation is well known. There are a variety of commercially available software packages that use variations of the above equation to generate aspheric lens designs. An example of these are: Super OSLO by Sinclair Optics, Inc., Code-V by Optical Research Associates and GENII-PC by Genesee Optics, Inc. These optical design programs are the most widely used packages available. Despite the different approaches used by the three methods, all packages have yielded identical results in aspheric lens design calculations. When used alone for vision correction, carefully designed elliptical lenses do provide an improved focus. However, when used in a system including the human eye, elliptical lenses are not significantly better than spherical lenses. This is because the eye contains a greater amount of aberration than the elliptical lens is able to correct as part of the overall corrective lens-eye system.
Methods used in the past to produce corrective lenses for the eye have resulted in lenses that are non-spherical. In U.S. Pat. No. 4,170,193 to Volk a lens is described which corrects for accommodative insufficiency by increasing dioptric power peripheralward. While this lens and other prior lens designs are not strictly spherical, it is not a pure asphere, and includes higher order deformation coefficients. This yields a surface which is radically different than that proposed herein. A flattening curve, such a hyperbola, would show a slight dioptric decrease peripheralward. Prior lens designs, while attempting to solve various optical problems by varying from a strictly spherical lens design, do not strive for improved vision by reducing the aberration of the image that strikes the retina of the eye.
An important reason for the common use of lens designs that have the above-noted limitations is the failure to take into account the effects of the entire lens-eye system. Lenses are usually designed as if the lens would be the only element that contributes to image aberrations, but there are may elements in the eye that affect image focus, such as the surfaces of the cornea and of the eye's natural lens. While the elliptical form was useful in reducing aberrations of the lens itself, when the lens is placed into a system containing all of the refracting surfaces of the human eye additional aspherical correction is required.